Discrete approximations to continuous distributions in decision analysis

dc.contributor.advisorBickel, J. Eric
dc.creatorHammond, Robert Kincaiden
dc.date.accessioned2014-07-01T19:46:35Zen
dc.date.issued2014-05en
dc.date.submittedMay 2014en
dc.date.updated2014-07-01T19:46:35Zen
dc.descriptiontexten
dc.description.abstractIn decision analysis, continuous uncertainties (i.e., the volume of oil in a reservoir) must be approximated by discrete distributions for use in decision trees, for example. Many methods of this process, called discretization, have been proposed and used for decades in practice. To the author’s knowledge, few studies of the methods’ accuracies exist, and were of only limited scope. This work presents a broad and systematic analysis of the accuracies of various discretization methods across large sets of distributions. The results indicate the best methods to use for approximating the moments of different types and shapes of distributions. New, more accurate, methods are also presented for a variety of distributional and practical assumptions. This first part of the work assumes perfect knowledge of the continuous distribution, which might not be the case in practice. The distributions are often elicited from subject matter experts, and because of issues such as cognitive biases, may have assessment errors. The second part of this work examines the implications of this error, and shows that differences between some discretization methods’ approximations are negligible under assessment error, whereas other methods’ errors are significantly larger than those because of imperfect assessments. The final part of this work extends the analysis of previous sections to applications to the Project Evaluation and Review Technique (PERT). The accuracies of several PERT formulae for approximating the mean and variance are analyzed, and several new formulae presented. The new formulae provide significant accuracy improvements over existing formulae.en
dc.description.departmentOperations Research and Industrial Engineeringen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/24941en
dc.language.isoenen
dc.subjectDiscretizationen
dc.subjectDecision analysisen
dc.subjectPearson systemen
dc.subjectJohnson systemen
dc.subjectProbability assessmenten
dc.subjectPERTen
dc.titleDiscrete approximations to continuous distributions in decision analysisen
dc.typeThesisen
thesis.degree.departmentOperations Research and Industrial Engineeringen
thesis.degree.disciplineOperations Research and Industrial Engineeringen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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